Effect of texture dispersion on the effective biaxial modulus of fiber-textured hexagonal, tetragonal, and orthorhombic films

The effective biaxial modulus (Meff) of fiber-textured hexagonal, tetragonal, and orthorhombic films is estimated by using the Voigt–Reuss–Hill and Vook–Witt grain-interaction models. The orientation distribution function with Gaussian distributions of the two Euler angles θ and ϕ is adopted to analyze the effect of texture dispersion degree on Meff. Numerical results that are based on ZnO, BaTiO3, and yttrium barium copper oxide (YBCO) materials show that the Vook–Witt average of Meff is identical to the Voigt–Reuss–Hill average of Meff for the (001) plane of ideally fiber-textured hexagonal and tetragonal films. The ϕ distribution has no influence on Meff of the (hkl)-fiber-textured hexagonal film at any θ distribution in terms of the isotropy in the plane perpendicular to the [001] direction. Comparably, tetragonal and orthorhombic films represent considerable actions of ϕ dispersion on Meff, and the effect of ϕ dispersion on Meff of a (001)-fiber-textured YBCO film is smaller than that for a (001)-fiber-textured BaTiO3 film since the shear anisotropic factor in the (001) shear plane of a YBCO film more closely approaches 1. Enhanced θ and ϕ distributions destroy the perfect fiber textures, and as a result, the films exhibit an evolution from ideal (hkl) fiber textures to random textures with varying full widths at half maximums of θ and ϕ.